On 10 May 2013, the concentration of climate-warming carbon dioxide in the atmosphere passed the milestone level of 400 parts per million for the first time in human history. The last time so much greenhouse gas was in the air was several million years ago, when the Arctic was ice-free, savannah spread across the Sahara desert and sea level was up to 40 metres higher than today.

The milestone moment was a sobering reminder that the emission of globe-warming gases is continuing unabated, despite ever more certainty that the burning of fossil fuels and deforestation is on track to end the millennia of relatively stable climate during which human civilisation has flourished.

In September, a landmark report on climate change science from the Intergovernmental Panel on Climate Change (IPCC) concluded it was “unequivocal” that global warming was the result of human actions. Its authors said that, without “substantial and sustained” emissions reductions, the 2C limit set by the world’s governments would be breached, resulting in heatwaves, droughts and more extreme weather. Ban Ki-moon, the UN secretary general, urged world leaders to pay heed to the “world’s authority on climate change” and forge a new global deal on cutting emissions. “The heat is on. Now we must act,” he said.

John Kerry, the US secretary of state, said: “This is yet another wake-up call: those who deny the science or choose excuses over action are playing with fire.”

The IPCC report, compiled by hundreds of the world’s climate experts, was the first for five years and also stated that sea levels are expected to rise a further 26-82cm by 2100, though a significant number of scientists think this is an underestimate. The IPCC also warned of the increasing acidification of the oceans as it absorbs CO2, with an October report finding the seas are becoming more acidic at the fastest rate in 300 million years and a mass extinction of species may already be almost inevitable.

The so-called “pause” in climate change – a slowing of the global air temperature rise over the last 15 years – was dismissed by IPCC co-chair Thomas Stocker, who said climate trends “should not be calculated for periods of less than 30 years.” Other scientists noted that excess heat has continued to be trapped by greenhouse gases and that just 1% of it heats the atmosphere, compared to 93% that warms the oceans. Another much-discussed issue – how sensitive the climate is to increases in atmospheric CO2 – turned out to make little difference to the temperature rises projected by the IPCC.

Excess heat has continued to be trapped by greenhouse gases and 93% warms the oceans. Photograph: Joe Raedle/Getty Images

The most controversial part of the IPCC report was its first statement on how much more CO2 humans can pour into the atmosphere without triggering dangerous levels of climate change – and the conclusion that more than half of that “carbon budget” has been used up.